1) a) The following table is intended to present five figure summaries [maximum, third

quartile, median, first quartile, minimum] of sets of data. Which two columns contain errors?

(3 marks)

A B C D

Max

125.0 60 9.76 20

Q3

47.3 17 6.84 8

Median

53.3 10 5.11 5

Q1

24.3 6 3.45 1

min

19.2 3 6.14 0

b) The following table is intended to present three figure summaries [ ( mean + sd), mean,

and (mean - sd) ] of sets of data. Which two columns contain errors?

(3 marks)

A B C D

mean +sd

7.33 6.68 31.18 7.73

mean

4.58 4.06 16.00 3.30

mean-sd

1.28 1.44 0.82 1.86

c)

A researcher who is interested in visual skills assesses 21 volunteer participants using a

simple ball control task. Each participant bounces a foam football on their fist. For a single

observed trial, the researcher records the number of bounces they achieve before losing

control of the ball. The scores recorded are given below.

10 38 17 4 35 33 7

35 8 8 12 7 3 13

4 60 5 15 11 6 5

Table 1

Ball skills assessment: scores for 21 Participants.

Give the mean, standard deviation, median and quartile points of these values.

(NB the sets of summary values given in parts a and b include the required values.)

(5 marks)

d)

Present a graph showing a three figure summary and the five figure summary on the same

axes. ( 7 marks)

e)

Which of these two representations of this data would you choose to use in a formal report?

Briefly, give a reason for your choice. (3 marks)

f)

A colleague of the researcher points out that the distribution of values is skewed. More

sensitive statistics can be applied to variables that are not skewed. How would you advise

the researcher to develop their test?

(4 marks)

2) Data for the performance of a sample of 18 students on a research methods course are

tabled below. The course assessment consists of two components a statistics test and a set of

reports.

Student Stats Pracs

a 14 11

b 28 28

c 45 37

d 48 53

e 51 43

f 55 58

g 56 58

h 59 59

i 61 43

j 61 46

k 62 58

l 65 57

m 66 47

n 67 59

n 68 50

p 69 40

q 78 59

r 82 62

a) Draw a scattergram to show the trends. (8 marks)

b) Which of the following values is closest to the Pearson product moment correlation

coefficient? (2 marks)

-0.203 0.008 0.416 0.806 0.952 1.203

c) Assuming the correlation coefficient is tabled above, what conclusion is supported?

(3 marks)

d) The lecturer then re computes the correlation coefficient with the data for two students

with low grades omitted. Which tabled alternative value is then closest to the computed

value?

(2 marks)

Selected critical values of the Pearson Product

Moment Correlation Coefficient.

2 tailed probability:

N of Pairs 0.10 0.05 0.02 0.01

140.458 0.532 0.612 0.661

160.426 0.497 0.574 0.623

180.400 0.468 0.543 0.590

200.378 0.444 0.516 0.561

220.360 0.423 0.492 0.537

240.344 0.404 0.472 0.515

e) Comment on the change in the result that occurs when the sample is reduced. (4 marks)

f) Suggest an alternative analysis that may have been used. (3 marks)

g) What should be considered as relevant to the choice of test? (5 marks)

3)Do women smile more than men?

Following an agreed protocol, 62 students each observe 8 pairs of people. At the time each

pair is in conversation in a public place. One person in each pair is covertly and carefully

observed for a period of just 10 seconds. The students select their pairs so that they each

observe 8 pairs of people, 2 of each of the possible combinations. [Male observed with a

female companion, Male observed with a male companion, Female observed with a male

companion and Female observed with a female companion.] The collated data are shown in

the table:

Sex of Observed P F F M M

Sex of companion f m f m Totals

N smiling 87 72 79 54 292

N not smiling 37 52 45 70 204

Total 124 124 124 124 496

Use this data to complete the 2x2 table below.

Observed Frequency F M Total

N smiling 292

N not smiling 204

248 248 496

a) What hypothesis is tested when a 2x2 Chi square is used to assess the trend shown in this

table?

(3 marks)

b) How many degrees of freedom are associated with the relevant critical value?

( 2 marks)

c) If there is no difference between the proportion of men and women smiling, how many

would there be in each cell?

(4 marks)

d) What is the difference between the observed and expected frequencies in each cell?

(NB with a single degree of freedom all differences are the same size. The total for each row

and column is zero.)

(2 marks)

Observed - Expected F M Total

N smiling 0

N not smiling 0

0 0 0

Expected Frequency F M Total

N smiling 292

N not smiling 204

248 248 496

e) Confirm the two given values as

(O-E)*(O-E) / Eand complete the table.

What is the total Chi Squared value?

(5 marks)

Observed F M Total

(O-E)*(O-E)/ E 1.16

(O-E)*(O-E)/ E 1.66

f) What conclusion would you expect in a formal report of this study?

(3 marks)

g) Give one guideline that would help a student select suitable participants.

( 3 marks)

h) Give one guideline that would help a student complete the observation of an

individual participant.

(3 marks)

4A researcher uses a computer based image processing system to merge a set of passport

style photographs of young women to form a single, composite image. She suspects that

such composites are more likely to be judged as attractive. To investigate this possibility she

asks participants to rate the attractiveness of a set of 12 images and a composite. Participants

are simply asked to place the pictures in order of judged attractiveness and the order for each

picture is recoded.

a) If the composite image tends to be judged as average attractiveness what is its expected

rank?

(2 marks)

Sample values of the two tailed Chi

distribution

df 5% 1% 0.10%

1 3.84 6.63 10.83

2 5.99 9.21 13.82

3 7.81 11.34 16.27

b) A sample of 19 participants complete the ranking. The judged rank attractiveness of the

composite is shown in the table (more attractive is higher rank). Use the table to complete a

suitable test to assess the hypothesis.

Atractiveness Ranking

P No Composite Expected

1 11

2 10

3 9

4 8

5 8

6 11

7 6

8 9

9 12

10 7

11 12

12 10

13 10

14 9

15 11

16 12

17 7

18 3

19 13

a) How many Participants rank the composite precisely ‘as expected’?

(2 marks)

b) How many Participants give the composite a lower rank than that expected?

( 2 marks)

c) Complete the Wilcoxon Matched Pairs Signed Ranks Test on this data.

(10 marks)

d) What conclusion is supported by this analysis?

(3 marks)

Critical Values for Wilcoxon signed rank test

NB SMALLER OBSERVED VALUES are associated with

LOWER significance levels.

Probability for two tailed test:

N of pairs 0.10 0.05 0.02 0.01

13 21 17 13 10

15 30 25 20 16

17 41 35 28 23

19 53 46 38 32

e) Suggest an alternative statistical analysis that could have been used.

(2 marks)

f) Give details of one factor that is relevant to choosing the most appropriate test statistic.

(4 marks)

**End of test**